Bivariate Data

Chapters 7-10

Formulas

Predicted Response Variable = Bo + B1(Explanatory Variable)

x

y

S

Srb 1 xbyb 10

x

y

S

Sr

When analyzing a scatterplot you will want to note strength, direction,form, and outliers.

Key Players:

r: Correlation – tells strength and direction of a linear relationship

r2: Coefficient of determination – tells the amount of variabilityin the Response variable explained by the LSRL or by the explanatoryvariable

bo: y-intercept – tells the starting point or the amount when the explanatory variable = 0. Can be an extrapolation.

b1: Slope – Rate of change, tells how much the response variablechanges when the explanatory variable goes up by 1 (or by the unitsIndicated on the x-axis)

Interpreting r, r2, b0, and b1

r = .99: Strong, positive linear relationship between time in hours and log of popr2 = .982: 98.2% of the variation in log of population is explained by hours or by the LSRLb1 = .115: As hours increases by 1, log of pop will increase by about .115

b0 = .322: When hours = 0, log predicted pop will equal .322, substituting 0 into

equation we get 103.22 = about 2.1 or predicted pop = about 2.1 thousand